Details

sample62.0ms

Algorithm

intervals

Results

32.0ms	79×	body	1280	valid
11.0ms	142×	body	80	valid
6.0ms	21×	body	640	valid
2.0ms	7×	body	320	valid
1.0ms	7×	body	160	valid

simplify21.0ms

Calls

1 calls:

Slowest

21.0ms

(- (atan (+ N 1)) (atan N))

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.7b

localize23.0ms

Local error

Found 2 expressions with local error:

1.9b	(- (atan (+ N 1)) (atan N))
0.0b	(atan (+ N 1))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
2×	`pow1` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16`
1×	`sub-neg` `flip3--` `diff-log` `diff-atan` `flip--` `distribute-lft-out--` `difference-of-squares`

Calls

2 calls:

Slowest

9.0ms	(- (atan (+ N 1)) (atan N))
1.0ms	(atan (+ N 1))

series14.0ms

Calls

2 calls:

Slowest

11.0ms	(- (atan (+ N 1)) (atan N))
3.0ms	(atan (+ N 1))

simplify276.0ms

Calls

12 calls:

Slowest

66.0ms	(/ (exp (atan (+ N 1))) (exp (atan N)))
42.0ms	(+ 1 (* (+ N 1) N))
30.0ms	(- (+ N 1) N)
24.0ms	(- (sqrt (atan (+ N 1))) (sqrt (atan N)))
23.0ms	(+ (sqrt (atan (+ N 1))) (sqrt (atan N)))

prune229.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize16.0ms

Local error

Found 3 expressions with local error:

0.3b	(atan2 1 (+ 1 (* (+ N 1) N)))
0.0b	(* (+ N 1) N)
0.0b	(+ 1 (* (+ N 1) N))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
3×	`pow1` `add-cbrt-cube` `associate-l` `add-exp-log` `insert-posit16` `add-log-exp`
2×	`flip3-+` `associate-*l/` `flip-+`
1×	`+-commutative` `*-commutative`

Calls

3 calls:

Slowest

7.0ms	(* (+ N 1) N)
3.0ms	(+ 1 (* (+ N 1) N))
0.0ms	(atan2 1 (+ 1 (* (+ N 1) N)))

series49.0ms

Calls

3 calls:

Slowest

32.0ms	(* (+ N 1) N)
12.0ms	(+ 1 (* (+ N 1) N))
5.0ms	(atan2 1 (+ 1 (* (+ N 1) N)))

simplify432.0ms

Calls

13 calls:

Slowest

74.0ms	(* (- (* N N) (* 1 1)) N)
55.0ms	(atan2 1 (+ N (+ (pow N 2) 1)))
47.0ms	(atan2 1 (+ N (+ (pow N 2) 1)))
46.0ms	(+ N (+ (pow N 2) 1))
38.0ms	(atan2 1 (+ N (+ (pow N 2) 1)))

prune421.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.3b

localize15.0ms

Local error

Found 3 expressions with local error:

0.3b	(atan2 1 (+ N (+ 1 (* N N))))
0.0b	(+ N (+ 1 (* N N)))
0.0b	(+ 1 (* N N))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

3×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16` `add-log-exp`
2×	`+-commutative` `flip3-+` `flip-+`
1×	`associate-+r+`

Calls

3 calls:

Slowest

2.0ms	(+ N (+ 1 (* N N)))
1.0ms	(+ 1 (* N N))
0.0ms	(atan2 1 (+ N (+ 1 (* N N))))

series25.0ms

Calls

3 calls:

Slowest

15.0ms	(+ 1 (* N N))
8.0ms	(+ N (+ 1 (* N N)))
3.0ms	(atan2 1 (+ N (+ 1 (* N N))))

simplify324.0ms

Calls

10 calls:

Slowest

58.0ms	(atan2 1 (+ N (+ (pow N 2) 1)))
55.0ms	(atan2 1 (+ N (+ (pow N 2) 1)))
51.0ms	(+ N (+ (pow N 2) 1))
44.0ms	(atan2 1 (+ N (+ (pow N 2) 1)))
36.0ms	(+ N (+ (pow N 2) 1))

prune367.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.3b

localize10.0ms

Local error

Found 4 expressions with local error:

13.3b	(sqrt (+ 1 (* (+ N 1) N)))
13.3b	(sqrt (+ 1 (* (+ N 1) N)))
0.3b	(atan2 1 (* (sqrt (+ 1 (* (+ N 1) N))) (sqrt (+ 1 (* (+ N 1) N)))))
0.0b	(* (sqrt (+ 1 (* (+ N 1) N))) (sqrt (+ 1 (* (+ N 1) N))))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

16×	`sqrt-div`
12×	`add-sqr-sqrt` `sqrt-prod`
10×	`*-un-lft-identity` `add-cube-cbrt`
9×	`pow1`
8×	`flip3-+` `flip-+`
6×	`add-cbrt-cube` `pow1/2` `associate-r` `associate-l` `add-exp-log`
4×	`frac-times` `insert-posit16` `add-log-exp`
2×	`rem-sqrt-square` `pow-prod-down` `associate-l/` `associate-r/` `pow-prod-up`
1×	`pow2` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod`

Calls

4 calls:

Slowest

7.0ms	(* (sqrt (+ 1 (* (+ N 1) N))) (sqrt (+ 1 (* (+ N 1) N))))
1.0ms	(sqrt (+ 1 (* (+ N 1) N)))
1.0ms	(sqrt (+ 1 (* (+ N 1) N)))
0.0ms	(atan2 1 (* (sqrt (+ 1 (* (+ N 1) N))) (sqrt (+ 1 (* (+ N 1) N)))))

series57.0ms

Calls

4 calls:

Slowest

21.0ms	(sqrt (+ 1 (* (+ N 1) N)))
18.0ms	(sqrt (+ 1 (* (+ N 1) N)))
13.0ms	(* (sqrt (+ 1 (* (+ N 1) N))) (sqrt (+ 1 (* (+ N 1) N))))
5.0ms	(atan2 1 (* (sqrt (+ 1 (* (+ N 1) N))) (sqrt (+ 1 (* (+ N 1) N)))))

simplify10.5s

Calls

58 calls:

Slowest

996.0ms	(sqrt (+ (pow 1 3) (pow (* (+ N 1) N) 3)))
938.0ms	(* (sqrt (+ (pow 1 3) (pow (* (+ N 1) N) 3))) (sqrt (+ (pow 1 3) (pow (* (+ N 1) N) 3))))
895.0ms	(sqrt (+ (pow 1 3) (pow (* (+ N 1) N) 3)))
770.0ms	(* (sqrt (- (* 1 1) (* (* (+ N 1) N) (* (+ N 1) N)))) (sqrt (- (* 1 1) (* (* (+ N 1) N) (* (+ N 1) N)))))
687.0ms	(sqrt (- (* 1 1) (* (* (+ N 1) N) (* (+ N 1) N))))

prune934.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.3b

regimes30.0ms

Accuracy

0% (0.0b remaining)

Error of 0.4b against oracle of 0.3b and baseline of 0.4b

bsearch1.0ms

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.5s	2814×	body	1280	valid
313.0ms	4035×	body	80	valid
212.0ms	662×	body	640	valid
106.0ms	299×	body	320	valid
28.0ms	190×	body	160	valid